Kreiner, C. F. and Zimmer, J., 2009. Travelling wave solutions for the discrete sine-Gordon equation with nonlinear pair interaction. Nonlinear Analysis: Theory Methods & Applications, 70 (9), pp. 3146-3158.
The focus of study is the nonlinear discrete sine-Gordon equation, where the nonlinearity refers to a nonlinear interaction of neighbouring atoms. The existence of travelling heteroclinic, homoclinic and periodic waves is shown. The asymptotic states are chosen such that the action functional is finite. The proofs employ variational methods, in particular a suitable concentration-compactness lemma combined with direct minimisation and mountain pass arguments.
|Item Type ||Articles|
|Creators||Kreiner, C. F.and Zimmer, J.|
|Uncontrolled Keywords||nonlinear klein-gordon lattice, travelling waves, calculus of variations, compactness, concentration|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||Zimmer_NATMA_2009_90_9_3146.pdf: NOTICE: this is the author’s version of a work that was accepted for publication in Nonlinear Analysis: Theory, Methods & Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis: Theory, Methods & Applications, Volume 70, Issue 9, 1 May 2009, DOI 10.1016/j.na.2008.04.018|
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